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Simplifying 2t2 + -9t + -4 = 0 Reorder the terms: -4 + -9t + 2t2 = 0 Solving -4 + -9t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -4.5t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.5t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -4.5t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.5t + t2 = 0 + 2 -4.5t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.5t + t2 = 2 The t term is -4.5t. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5t + 5.0625 + t2 = 2 + 5.0625 Reorder the terms: 5.0625 + -4.5t + t2 = 2 + 5.0625 Combine like terms: 2 + 5.0625 = 7.0625 5.0625 + -4.5t + t2 = 7.0625 Factor a perfect square on the left side: (t + -2.25)(t + -2.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (t + -2.25) equal to 2.657536453 and -2.657536453.Subproblem 1
t + -2.25 = 2.657536453 Simplifying t + -2.25 = 2.657536453 Reorder the terms: -2.25 + t = 2.657536453 Solving -2.25 + t = 2.657536453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 2.657536453 + 2.25 t = 2.657536453 + 2.25 Combine like terms: 2.657536453 + 2.25 = 4.907536453 t = 4.907536453 Simplifying t = 4.907536453Subproblem 2
t + -2.25 = -2.657536453 Simplifying t + -2.25 = -2.657536453 Reorder the terms: -2.25 + t = -2.657536453 Solving -2.25 + t = -2.657536453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -2.657536453 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -2.657536453 + 2.25 t = -2.657536453 + 2.25 Combine like terms: -2.657536453 + 2.25 = -0.407536453 t = -0.407536453 Simplifying t = -0.407536453Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.907536453, -0.407536453}
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